2.2 “Slope & Rate of Change” Slope of a Line: Slope: m = 𝒚𝟐 − 𝒚𝟏 𝒙𝟐 − 𝒙𝟏 Rate of Change: 𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑪𝒉𝒂𝒏𝒈𝒆 𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑪𝒉𝒂𝒏𝒈𝒆 = 𝑹𝒊𝒔𝒆 𝑹𝒖𝒏
Examples A skateboard ramp has a rise of 15 inches and a run of 54 inches. What is the slope? What is the slope of the line passing through the points (-2, 1) and (3, 5)? ***Label the points, reduce if possible, and leave as a fraction.
Classification of Lines By Slope Positive Slope: Negative Slope: Zero Slope: Undefined Slope:
Practice Find the slope of the line that passes through the given points: (3, 4) (6, -8) (7, -4) (12, -4) (1, 2) (-1, -8) (-3, 7) (-3, -5)
Parallel & Perpendicular Lines Parallel Lines: The slopes are the same. Perpendicular Lines: The slopes are opposite reciprocals.
Example Determine whether the lines are parallel, perpendicular or neither: 3y = x – 3 2y = – 6x – 12 Steps: Put each equation into slope intercept form. y = mx + b Determine whether parallel or perpendicular by looking at the m’s of both equations. If you are given points instead of lines, find the slope of each.
Practice 10y = – 2x – 10 5y = – x (1, 2) (-1, -8) & (0, 3) (5,4) (1, 2) (-1, -8) & (0, 3) (5,4) 4. (3, 4) (-3, 0) & (2, 1) (4, -2)
Word Problem
Finding Missing Values 1. Find the value of “k” so that the line through (k, 6) & (-7, 3) has a slope of 𝟑 𝟒 2. Find the value of “k” so that the line through (2k + 2, 1) & (k, 3) has a slope of −𝟐 𝟑